Internal problem ID [12697]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {3 y}{t}=2 \,{\mathrm e}^{2 t} t^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t)-3/t*y(t)=2*t^3*exp(2*t),y(1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -t^{3} \left (-{\mathrm e}^{2 t}+{\mathrm e}^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 20
DSolve[{y'[t]-3/t*y[t]==2*t^3*Exp[2*t],{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (e^{2 t}-e^2\right ) t^3 \]